﻿Bowed 
  Stringed 
  Instruments. 
  495 
  

  

  Griitay 
  and 
  De 
  Haas 
  to 
  their 
  observations 
  (Proc. 
  Roy. 
  Soc. 
  

   Amsterdam, 
  January 
  1910) 
  requires 
  revision. 
  As 
  a 
  matter 
  

   of 
  fact, 
  it 
  appears 
  from 
  my 
  detailed 
  observations 
  that 
  Griitay 
  

   and 
  De 
  Haas 
  were 
  in 
  error 
  in 
  assuming 
  that 
  the 
  motion 
  of 
  

   the 
  bridge 
  in 
  its 
  own 
  plane 
  is 
  practically 
  that 
  of 
  a 
  rigid 
  body. 
  

   Owing 
  to 
  the 
  form 
  of 
  the 
  bridge, 
  the 
  cuts 
  in 
  it, 
  &c., 
  this 
  is 
  

   very 
  far 
  indeed 
  from 
  being 
  the 
  case, 
  the 
  elastic 
  distortions 
  

   being 
  very 
  large. 
  For 
  instance, 
  it 
  makes 
  all 
  the 
  difference 
  

   in 
  the 
  pitch 
  of 
  the 
  wolf 
  if 
  a 
  load 
  be 
  fixed 
  immediately 
  above 
  

   instead 
  of 
  immediately 
  below 
  the 
  cut 
  on 
  the 
  G-string 
  side 
  of 
  

   the 
  bridge. 
  This 
  fact 
  is 
  inconsistent 
  with 
  the 
  supposition 
  

   made 
  by 
  Griitay 
  and 
  De 
  Haas 
  that 
  the 
  motion 
  of 
  the 
  bridge 
  

   in 
  its 
  own 
  plane 
  is 
  one 
  of 
  simple 
  rotation 
  about 
  an 
  axis, 
  and 
  

   proves 
  that 
  the 
  theory 
  of 
  the 
  action 
  of 
  the 
  mute 
  put 
  forward 
  

   by 
  these 
  writers 
  is 
  untenable. 
  

  

  6. 
  In 
  view 
  of 
  what 
  has 
  been 
  said 
  in 
  para. 
  4, 
  the 
  observed 
  

   muting 
  of 
  the 
  high 
  notes 
  of 
  the 
  instrument 
  which 
  Mr. 
  Giltay 
  

   suggests 
  as 
  a 
  difficulty, 
  is 
  easily 
  seen 
  to 
  be 
  exactly 
  what 
  is 
  to 
  

   be 
  expected 
  according 
  to 
  the 
  view 
  of 
  the 
  action 
  of 
  the 
  mute 
  

   put 
  forward 
  by 
  me. 
  In 
  the 
  absence 
  of 
  a 
  mute, 
  the 
  resonance 
  

   of 
  the 
  violin 
  is 
  by 
  far 
  the 
  strongest 
  at 
  the 
  pitch 
  of 
  the 
  

   two 
  wolf-notes. 
  Theory 
  thus 
  indicates 
  that 
  the 
  quality 
  of 
  

   violin-tone 
  and 
  the 
  effect 
  of 
  a 
  mute 
  upon 
  it 
  may 
  be 
  cha- 
  

   racterized 
  as 
  follows 
  : 
  the 
  gravest 
  tones 
  have 
  a 
  weak 
  funda- 
  

   mental 
  with 
  strong 
  second 
  and 
  third 
  harmonics, 
  muting 
  

   increasing 
  the 
  fundamental 
  at 
  the 
  expense 
  of 
  the 
  harmonics: 
  

   in 
  the 
  middle 
  of 
  the 
  scale 
  the 
  tones 
  should 
  have 
  strong 
  

   fundamental 
  and 
  second 
  harmonic 
  with 
  relatively 
  weak 
  

   higher 
  harmonics, 
  all 
  except 
  the 
  fundamental 
  being 
  decreased 
  

   by 
  muting; 
  the 
  highest 
  tones 
  should 
  have 
  strong 
  fundamental 
  

   and 
  weak 
  upper 
  partials, 
  all 
  the 
  components 
  being 
  decreased 
  

   by 
  muting. 
  The 
  observations 
  of 
  Hewlett 
  (Physical 
  Review, 
  

   Xov. 
  1912) 
  and 
  those 
  of 
  Edwards 
  already 
  quoted 
  are 
  in 
  

   substantial 
  agreement 
  with 
  the 
  above. 
  

  

  7. 
  Another 
  interesting 
  question 
  which 
  arises 
  regarding 
  

   the 
  action 
  of 
  the 
  mute 
  is 
  its 
  effect 
  on 
  the 
  minimum 
  bowing- 
  

   pressure 
  necessary 
  in 
  order 
  to 
  elicit 
  a 
  steady 
  vibration 
  of 
  the 
  

   usual 
  type. 
  I 
  have 
  investigated 
  this 
  question 
  theoretically 
  

   by 
  considering 
  the 
  effect 
  of 
  the 
  mute 
  on 
  the 
  motion 
  of 
  the 
  

   bridge 
  and 
  consequently 
  on 
  the 
  minimum 
  frictional 
  force 
  

   which 
  should 
  be 
  exerted 
  by 
  the 
  bow 
  on 
  the 
  string 
  in 
  order 
  

   that 
  a 
  steady 
  vibration 
  should 
  be 
  possible. 
  The 
  question 
  has 
  

   also 
  been 
  studied 
  experimentally 
  using 
  a 
  mechanical 
  player 
  

   in 
  which 
  an 
  ordinary 
  violin 
  bow 
  excites 
  the 
  strings 
  of 
  a 
  

   violin 
  under 
  strictly 
  controlled 
  pressure 
  and 
  velocity 
  of 
  

   movement. 
  The 
  quantitative 
  data 
  obtained 
  clearlv 
  show 
  the 
  

  

  2 
  M 
  2 
  

  

  